Which of the following correctly describes the tangent function?

The tangent function is defined as the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. This relationship can be summarized using the formula:

[

\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}

]

In the context of a right triangle, if you take any acute angle (theta), the side opposite that angle is referred to as the "opposite" side, while the side that is next to that angle and not the hypotenuse is referred to as the "adjacent" side.

The other choices do not accurately represent the tangent function. The choice describing the opposite over the hypotenuse corresponds to the sine function, while the adjacent over the hypotenuse relates to the cosine function. Lastly, the hypotenuse over the adjacent does not correspond with any of the primary trigonometric functions in the context of a right triangle. Understanding these ratios is crucial when applying trigonometric functions to solve problems involving angles and sides in triangles.